Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions

TL;DR

This paper demonstrates the classical and quantum integrability of type II superstring sigma-models on AdS backgrounds with Ramond-Ramond flux, using supercoset constructions and formalisms like Green--Schwarz and pure spinor.

Contribution

It constructs Lax connections for superstring models in various AdS backgrounds and proves their classical and quantum integrability, including the effects of D-branes and BRST symmetry.

Findings

Existence of a one-parameter family of flat currents indicating integrability.

Proof of quantum integrability via BRST symmetry in pure spinor formalism.

Confirmation of one-loop conformal invariance from ppa-symmetry.

Abstract

We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: non-critical superstrings on AdS_{2d} and critical superstrings on AdS_p\times S^p\times CY. We work both in the Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter family of flat currents (a Lax connection) leading to an infinite number of conserved non-local charges, which imply the classical integrability of both sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigma-model. We discuss how classical \kappa-symmetry implies one-loop conformal invariance. We consider the addition of space-filling D-branes to the pure spinor formalism.